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Unformatted text preview: h Algwnﬁem 1 ﬂﬁjafcw YORK UNIVERSITY
Arts Economics 2300 D: Barry Smith
Final Exam
Fall 2005 Instructions. The exam consists of 3 parts: A, B and C. Part A contains
choice and is worth 12 marks. Part B contains no choice and is worth 16 points.
Part G contains choice and is woth 32 marks. You have 3 hours to complete
this exam soI roughly speaking, you have 36 minutes for part A, 44 minutes for
part B and 100 minutes for part C. Write your answers in the exam booklets that have been supplied to you. Be sure to provide the information requested
at the front of the exam booklets. Part A
Answer 2 of the following 4 questions. Each question involves a
statement that may or may not be true. Be sure to deﬁne any technical terms entering the questions. Each is worth 6 marks.
,4 1. In order for preferences to exhibit a diminishing marginal rate of substi— tution, it is necessary that both goods have diminishing marginal utilities.
(Hint: Think about positive monotonic transformations of utility func- Bert)» tions 2. Demand functions are homogeneous of degree zero in prices and income
only if the preferences are Cobb—Douglas. If preferences are homothetic then no goods can be inferior. 4. If the preferences of an agent have a diminishing marginal rate of substi- V tution then the agent wiil work more if she is offered a higher wage for
I Q ' working overtime hours. Part B
Answer the following question. It is worth 16 marks. 1. Suppose that an agent has standard preferences with a diminishing marginal
rate of substitution. There are two goods: 3;; and $2 with prices 101 and
p2. The income of the agent consists of endowments of the good in the
amounts: wl and wg. Suppose that good 1 is inferior. K J ‘ - M 41‘ (a) Show the consumer equilibrium on a carefully labelled diagram. Ex— 3 0‘) ‘HI (
10! Ml MM 3 ‘1 plain why the point that you Show is an equilibrium. /
LGAW‘l' (r‘F‘F (7/1" Mal/hi” (b) Suppose that the price of good 1 (p1) increases. Explain the income, " /2
substitution and endowment effects and illustrate all of them using :7 a CAREFULLY labelled diagram.
" lair“ ms were [7139f ) (c) Express the results in terms of rates of change using the Slutsky equation. Identify all of the terms.
Wt? mm
M, M Part C
Answer 4 of the following 5 questions. Each question is worth 8
marks. 1. A consumer has interternporal preferences given by the utility function:
U (01,02) 2 min[Cl,2C2]. The consumer has income each period equal
to $100 and can borrow and save at the interest rate r = .1. (a) Solve for the intertemporal consumptions that maximize utility. Il—
lustrate your results using a carefullty labelled diagram. (b) Using carefully labelled diagrams, show that, in general, an increase
in the interest rate T will make a saver better off. (c) In this special case can you tell what would happen to the level of
utility of an agent who was initially a borrower? \ 2. A consumer has preferences given by U{:r1, :62) = (a) Derive the demand curves for :31 and 332 when prices and income are
given by $1,332 and m. (b) Illustrate the equilibrium on a diagram when p1 2 p2 = $1 and
I = $10. ((2) Calculate the exact income and substitution effects for 3:1 when p1
rises to $2. Show all steps. Note: no marks will be given for a purely
diagrammatic answer but your results must be illustrated with a
carefully iabelied diagram. 3. A consumer has preferences given by U(:1:,y) = my. (a) Calculate the equilibrium quantities of :r and y when pm 2 $2, gay 2 $3
and I = 12. (b) Suppose p2 increases to $3 when a per unit tax of $1 is placed on 2:.
What is the new value of m and how much tax revenue is raised? (c) Suppose that the same tax revenue is raised by an income tax as
opposed to a per unit tax. Show that, in general, the consumer is
better off. Show it is true in this example as well. bidl‘ ?W’ ’1’" (cal Mﬂhr‘v ’ C its/WW ,‘ 4. A consumer has preferences over wealth given by U(W) = W"5 The con- sumer’s initial wealth is $100 and she faces a loss of $51 with probability
2 .25. (a) Deﬁne the term risk aversion. Is this agent risk averse? Illustrate
your results in a carefully laballed diagram. (b) What is the expected income of the consumer? (c) What is the largest premium that the consumer will pay to insure
against the loss of $51? 5. Consider a stardard labour supply model of an agent who has an endow—
ment of time equal to R and an endowment C' of a consumption good.
Suppose that the price of the consumption good is p and that the wage
rate equals '41). Suppose that the government is thinking about giving
workers a per unit subsidy of s for every hour worked. One economist
(from the University of Toronto) claims that, as a result of this subsidy,
each agent will want to work more hours. Do you agree? Answer this question using a carefully labelled diagram. You may assume that leisure
is a normal good. / 712% MT W WE‘MMLk J...” m AWN“ Nﬂ Cm » t *_ - WW
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